Lattice Boltzmann simulation of immiscible fluid displacement in porous media: Homogeneous versus heterogeneous pore network

Carbon capture and storage (CCS) is a method of reducing anthropogenic emission of greenhouse gases into the atmosphere thereby mitigating global climate change. In CCS, carbon dioxide (CO2) is captured from power plants or other large point-source emitters, purified, compressed, and injected into subsurface formations for long-term sequestration. Deep saline aquifers are considered as the most ideal candidate reservoirs for sequestering CO2 because they are geographically widespread, have large potential capacities for storage, and are not used for water supply.1 When CO2 is injected into deep saline aquifers, it exists in a supercritical state and displaces the formation fluid from the pore space in a variety of possible saturation patterns, depending on the relative strength of capillary and viscous forces, as well as large and small scale geological heterogeneities.2–4 Fingering and displacement patterns at the pore scale strongly influence the CO2 storage process within the reservoir in terms of storage capacity, security, and ultimate fate of the injected CO2. Therefore, it is of paramount importance to study and understand the mechanisms of immiscible fluid displacement in realistic porous media.

Experimental studies of immiscible fluid displacement focus on using two categories of porous media: natural media, such as rock cores and transparent network models collectively known as micromodels. Rock cores are advantageous for characterizing individual formations, but suffer from difficulty in monitoring fluids at the pore scale since sophisticated and unique micro-tomographic facilities are needed to visualize the internal distribution of the fluids within the rock cores. Moreover, it is challenging to independently manipulate porosity, pore size, connectivity, and wetting properties for natural porous media. These limitations can be overcome by micromodels, which are two-dimensional (2D) pore network patterns etched into materials such as silicon, glass, polyester resin, and most recently, polydimethylsiloxane (PDMS).5 Micromodels allow for visualization of fluid distribution using cameras with or without fluorescent microscopy, and subsequent quantification of fluid saturation and interfacial area may provide mechanistic insight about physical displacement process at the microscopic level. For example, Lenormand et al.6 performed a series of classic displacement experiments for several fluid pairs in an oil-wet micromodel constructed of a polymer resin, and established a phase diagram delineating parameter domains for stable displacement, capillary, and viscous fingering. They also observed “crossover” behavior in intermediate regions of their phase diagram corresponding to flow morphologies with characteristics of more than one regime. Phase diagram behavior was later demonstrated by Zhang et al.7 in a homogeneous water-wet micromodel, and their experimental results showed that the exact locations of the various region boundaries and crossover zones are dependent on the pore network. Micromodels, however, are criticized for the lack of the complex geometry of real media, which often has multiscale and random characteristics that will dictate fluid and solute transport. Numerical simulations can complement experimental studies, providing an economic and efficient pathway to explore the influence of flow and physical parameters in various complicated porous media. However, the numerical methods based on the continuum description are insufficient to consider the influence of pore-scale parameters on the macroscopic bulk properties and, hence, the details of fingering pattern in the porous media cannot be resolved.8 Statistical models, i.e., Invasion Percolation (IP), Diffusion-Limited Aggregation (DLA), and anti-DLA, are able to describe certain “specialized” displacement regimes, but they cannot capture transitions from one regime to another.6,9

The lattice Boltzmann method (LBM) has been developed as an attractive and promising numerical tool for pore-scale simulation of multiphase flows in porous media.10–14 Unlike pore-network models,6,15,16 which use a simplified representation of pore geometry and approximate transient flow with a steady-state Poiseuille law, LBM models complex multiphase flows in domain with realistic pore geometries. The fundamental idea of the LBM is to construct simplified kinetic models that incorporate the essential physics of microscopic or mesoscopic processes to ensure that the macroscopic averaged properties obey the desired macroscopic equations. LBM has several advantages over the conventional grid-based computational fluid dynamics (CFD) methods, such as volume-of-fluid (VOF)17,18 and level-set (LS) methods,19,20 especially in dealing with complex boundaries, incorporation of microscopic interactions, flexible reproduction of interface between multiple phases, and parallelisation of the algorithm. In the LBM community, a number of multiphase models have been proposed. These models can be classified into four types, i.e., the color-fluid model,21–23 the interparticle-potential model,24–26 the phase-field-based model,27,28 and the mean-field theory model.29 A detailed review of these models for pore-scale flows can be found in Ref. 30.

In this paper, a recently improved color-fluid LB model23 is used to simulate immiscible displacement of a wetting fluid by injecting a non-wetting fluid at a constant flow rate under a wide range of flow conditions in two microfluidic flow cells, one with a homogeneous pore network and the other with a randomly heterogeneous pore network. We investigate the effect of capillary number, viscosity ratio, and media heterogeneity on displacement patterns. We also quantify the fluid saturations and interfacial areas, and compare the simulation results with the experimental results of Zhang et al.,7 who conducted a series of displacement experiments in a homogeneous pore network micromodel with precisely microfabricated pore structures.